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General Relativity for the Gifted Amateur: errata

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General Relativity for the Gifted Amateur: errata

When you find errors in the book we would be grateful if they could be emailed to tom.lancaster_at_durham.ac.uk.

Corrections to the scientific content

We recommend that you correct the following errors in your copy of the book.

  • Page 7, eqn 7: missing factor of 31/2 on the right hand side.
  • Page 48, sidenote 9: the position of the subscript ‘0’ and label ‘obs’ should be swapped, such that ‘0’ becomes the superscript.
  • Page 53, below 4.51: the variable given as rho on the right hand side of the expression, should be a p.
  • Page 58, sidenote 7: y = r cosθ should read r sinθ.
  • Page 94: eqn 8.17: the first term on the right-hand side of the second equation is missing a factor cosθ.
  • Page 98, eq. 8.38 should read dr/dt = [(r – 2GM)/(r + 2GM)]1/2.
  • Page 103 , eqn 9.9: inside the bracket on the right-hand-side, the factor of dr/dλ should be squared.
  • Page 104, eqn 9.23: the index μ in the variable xμ on the right-hand-side should be ν.
  • Page 105: Eq. (9.36) the expression for Γvuu should have a in the denominator rather than u.
  • Page 112, eqn 10.28, the subscript “r-hat” on the “e” should be “θ-hat”.
  • Page 123: Example 11.2, second derivative of si halfway down the final paragraph: delete factor of m on the left-hand side.
  • Page 127: Two instances of “(3,1)” should be “(1,3)”.
  • Page 129, eqn 11.38: missing minus sign on right-hand side.
  • Page 164, sidenote 22: a(t0) should be squared.
  • Page 166, eqn 15.32: dt should be squared.
  • Page 166, penultimate paragraph Tμ should read Tμν.
  • Page 171, sidenote: in the penultimate equation for the spatial components of the Ricci tensor, the final term should be 2k/a2, rather than 2k/a.
  • Page 177, caption to Fig 16.6: tob+δtem should read tob+δtob.
  • Page 179, exercise 16.4(c): In eq (16.54), Rrr = Λ’/r should be 2Λ’/r. In part (d), the first part of eqn 16.55 should read, Λ’ = Kr exp(2Λ). In the second part, the factor in exp(-Λ) should read exp(-2Λ).
  • Page 181:2 lines before eqn 17.1: the potential energy should be written V=-GMm/r, rather than U.
  • Page 182, sidenote: in the penultimate equation for the spatial components of the Ricci tensor, the final term should be 2k/a2, rather than 2k/a. This correction is also required in the first line of eqn 17.5.
  • Page 185, eqn 17.23: insert a factor of 2 in front of ρr(0) .
  • Page 185, eqn 17.31: the right-hand side should be multiplied by a factor H02.
  • Page 186, two lines before eqn 17.30: the expression for ρc(0) should read 3H02/8π.
  • Page 200, eqn 18.50: the equation for T should include the factor (1-x2) rather than (1-x).
  • Page 205, caption to Fig 19.6: remove prime from r‘ and t‘.
  • Page 209, line after eqn 19.21: the variable t and r should be primed.
  • Page 214, eqn 19.37: sin2φ should read sin2χ.
  • Page 219, sidenote 4, eqn 20.2: In the 4th term of the right hand side of the first line, the dot should be removed from r (i.e. we do not take the time derivative of this variable in this term).
  • Page 224, text above eqn 20.36: there should be a factor r12 in the denominator for K1.
  • Page 224, eqn 20.37: the prefactor should be K1/u1, rather than u1/K1.
  • Page 226: Caption to Fig 20.8(c): should read n>-1.
  • Page 233, eqn 21.28: insert minus sign on the right-hand side.
  • Page 235, eqn 21.39: insert factors of 2 in front of Φ and Λ in the exponentials.
  • Page 236, exercise 21.8: remove factors of 8π from the given components of Tμν.
  • Page 239, section 22.2, line 6: insert minus sign on the right-hand side of the in-line equation.
  • Page 242, sidenote 14: insert a factor 1/r before the components of eθ and a factor 1/rsinθ before the components of eφ.
  • Page 248, eqn 23.5: in the first bracket, r should be r+.
  • Page 248, eqn 23.9: on the right-hand side, r+ should not be squared.
  • Page 250, sidenote 8: the formula towards the end should read u0²(1 – ε²) = -2Em/L² (i.e. the square on u0 is missing).
  • Page 250, just before eq. 23.21: “we write ε²u0² = …” (i.e. the ε should be squared).
  • Page 251, eqn 23.22: the first = sign should be a + sign.
  • Page 253, eqn 23.32: On the right-hand side, Ẽ should be squared.
  • Page 254, sidenote 3, line 2: remove square root sign.
  • Page 257, eqn 24.22: 2cosφ should be cos2φ. Int the text below this, “Total deflection Δφ” should read “deflection δφ”. In equation 24.23, Δφ should then read δφ.
  • Page 266, eqn 25.10: replace the + sign with a – sign.
  • Page 268, sidenote 15: insert a – sign on the right-hand side of the first equation.
  • Page 277, eqn 26.26: the term +2dUdr should read -2dUdr.
  • Page 278, eqn 26.34: Ur should read ur.
  • Page 292, sidenote 12: the reference should be to eqn 28.11, rather than 28.12.
  • Page 294, sidenote 17, eqn 28.21: replace the two instances of -dW with +dW.
  • .Page 449, eqn 41.9: in the the first term on the right-hand side, φ should not be squared.
  • Page 554, eqn A1: all terms on the right-hand-side should be squared.
  • Page 562: sidenote 4: “covariant” should read “contravariant”.
  • Page 563: “contravariant” should read “covariant”.
  • Page 584, eqn D.20 and following line: the variable θ should be φ.
  • Page 588, problem 4.4: in the equation,  r = x2 + y2 + z2, the radius r should read  r2.
  • Page 589, problem 4.4, in the second of eqns E.23, a factor of r is missing from all three of the terms on the right-hand side.
  • page 591, eqn E.71: there is an additional nonzero connection coefficient: Γrtt = –Ωr².
  • Page 595, question 18.6(c): the equation for the hyperbolic curve should read T2–X2=1.
  • Page 595, question 18.8: the factors (1-x) should read (1-x2).
  • Page 598, question 23.4: insert a factor of 2 before the middle term in the brackets on the right-hand side.
  • Page 599, eqn E.214: There should be a factor 1/L̃ before the brackets.

With grateful thanks to John Camm, Jay Epstein, Zhanzhi He, Joey LH Ooi and Leslie Rysdale.

Last updated 08/11/25